The present invention relates to acoustic equalization and in particular to filters used for acoustic equalization.
Loudspeaker-room acoustic equalization is a challenging problem to solve with realizable digital equalization filters, especially at lower frequencies (for example, less than 300 Hz). A typical room is an acoustic enclosure which may be modeled as a linear system. When a loudspeaker is placed in the room, the resulting response is the convolution of the room linear response and the loudspeaker response and may be denoted as h(n); nε{0, 1, 2, . . . }. This loudspeaker-room impulse response has an associated frequency response, H(ejω) (i.e., H(z)), which is a function of frequency. Generally, H(ejω) is also referred to as the Loudspeaker-Room Transfer Function (LRTF). In the frequency domain, the LRTF shows significant spectral peaks and dips in the human range of hearing (for example, 20 Hz to 20 kHz), in the magnitude response, causing audible sound degradation at a listener position.
FIG. 1 shows the LRTF (unsmoothed 10 and third-octave smoothed 12) of the loudspeaker-room response. As is evident from the ⅓-octave smoothed magnitude response plot 12, the loudspeaker-room response exhibits a large gain of about 10 dB at 75 Hz and the peak is about an octave wide which will result in unwanted amplification of sound in this region. A notch at around 145 Hz about a half-octave wide will attenuate sound in this region. Additional variations are present throughout the frequency range of hearing (20 Hz-20 kHz), and a non-smooth and non-flat envelope of the response, result in a poor sound reproduction from the loudspeaker in the room where the room linear response and the loudspeaker response h(n) was measured.
An equalization filter may be applied to correct such response variations in the frequency domain (i.e., minimize the deviations in the magnitude response to obtain a flat response) and ideally also minimize the energy of the reflections in the time domain. Known approaches include using psychoacoustic warping where the equalization filter is designed on a warped frequency axis (i.e., the perceptual Bark scale) of the room response function with a lower order model (for example, linear predictive coding). Other similar approaches using low-order spectral modeling and warping are described in:    M. Karjalainen, E. Piirilii, A. Jarvinen, and J. Huopaniemi, “Comparison of Loudspeaker Response Equalization Using Warped Digital Filters,” Journal of Audio Eng. Soc., 47 (1/2), pp. 15-31, 1999;    M. Karjalainen, A. Harma, U. K. Laine, and J. Huopaniemi, “Warped Filters and Their Audio Applications,” Proc. 1997 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA '97), New York, 1997; and    A. Harma, M. Karjalainen, L. Savioja, V. Valimaki, U. K. Laine, and J. Huopaniemi, “Frequency-Warped Signal Processing for Audio Applications,” Journal of Audio Eng. Soc., vol. 48, no. 11, pp. 1011-1031, November 2000.